Self-healable printed magnetic field sensors using alternating magnetic fields

We employ alternating magnetic fields (AMF) to drive magnetic fillers actively and guide the formation and self-healing of percolation networks. Relying on AMF, we fabricate printable magnetoresistive sensors revealing an enhancement in sensitivity and figure of merit of more than one and two orders of magnitude relative to previous reports. These sensors display low noise, high resolution, and are readily processable using various printing techniques that can be applied to different substrates. The AMF-mediated self-healing has six characteristics: 100% performance recovery; repeatable healing over multiple cycles; room-temperature operation; healing in seconds; no need for manual reassembly; humidity insensitivity. It is found that the above advantages arise from the AMF-induced attraction of magnetic microparticles and the determinative oscillation that work synergistically to improve the quantity and quality of filler contacts. By virtue of these advantages, the AMF-mediated sensors are used in safety application, medical therapy, and human-machine interfaces for augmented reality.

Energy-dispersive X-ray Spectroscopy (EDX) maps of Ni81Fe19 microparticles. Elements of Ni and Fe distribute uniformly over the microparticles. Scale bars: 30 μm.  The results confirm the elastic behavior of all samples, given that the storage moduli are higher than loss moduli over the entire frequency range. The elasticity for the composite made of pure PDMS is due to covalently crosslinked polymer networks. The addition of high amount of PBS introduces the relaxation processes of the composite around 1 rad/s. This behavior is caused by the relaxation of supramolecular network of PBS. The higher amount of PBS, the more pronounced the effect of PBS relaxation. Pure PBS behaves as viscous liquid at long time scale and flows.
Fortunately, even 10% of crosslinked PDMS can provide mechanical stability 2 . Note that, the microparticle volume fractions of the measured composites are only about 12%. With the addition of more microparticles, the mechanical stability can be further enhanced due to the confinement of microparticles matrix 3 . Fig. S4 Characterization of the AMF setup. a) Photograph and b) schematic illustration of solenoid used for generating AMF. c-e) Temporal evolution of the magnetic field measured at different locations, e.g., sites 1 -3 indicated in a). A commercial Hall-effect sensor was used for calibration. For assuring the measurement uniformity, magnetoresistive composites were printed on commercial flat flexible cables. Each cable has ten measurement pads and the inter-pad distance are about 0.4 mm. Two-point configuration was used to measure the electrical conductivity. In other words, nine conductivity values were measured for every type of composite. The composite thicknesses were about tens of to hundreds of micrometers. Fig. S6 Electrical circuit consisting of a printed magnetoresistive sensor, a LED, and a resistor. a) Schematic illustration. b) Photograph of all elements on printed circuit board. As of the sensor, the applied composite solution had the 1 g/ml concentration and the conductive pad was made of commercial conductive silver composite.
Fig. S7 Self-healing of magnetoresistive sensor by thermal treatment. a) Schematic illustration and b) microscopic photograph of magnetoresistive composite (from left to right): original, cutting by a blade, manual reassembly, and heating for 60 min at 120 o C. Scale bars: 200 μm. c) Electrical resistance and d) magnetoresistance of the sensor before and after healing. The magnetoresistive sensor was fabricated on Si wafer by pipetting composite solution with 0.4 g/ml of Ni81Fe19 microparticles. Other fabrication procedures were the same with that stated in the Methods section. Continuous measurement of the a) electrical resistance and b) magnetoresistance as a function of time. Inset: Configuration of measurement. The resistance was increased when the sample was exposed to magnetic field. The sensor response to magnetic field was stable after the self-healing process and did not change even after 2500 s of measurement.     Simulation of electric potential in magnetoresistive composite was performed by the ACDC module of COMSOL Multiphysics. The simulation of electrical potential follows stationary current conversion equations: where J, E, V and σ are the current density, electric field, electric potential and electrical conductivity in the active materials of magnetoresistive composite, respectively; Je is an externally generated current density.   In panels c) and d), the temperature of the sensor was changed from 19.5 to 21.5 o C after applying AMF for 1 min. The small variation of temperature is in good accordance with magnetic hysteresis loop of magnetoresistive composite in Supplementary Fig. 17, proving that negligible heat was generated in the soft magnetic materials (here, Ni81Fe19 microparticles). In other words, the temperature increase (about 2 o C) mainly stemmed from the heat accumulation in the metal bar of AMF oscillator during operation and thus should not be responsible for the electrical decrease observed in Fig. 1b.

Fig. S25 Magnetoresistive sensors in water. Sensors a) being placed and b) working in water. c)
Magnetoresistance variation of a magnetoresistive sensor after carrying out cutting/healing in water for two times. d) Screenshots of Supplementary Movie 3, recording the AMF-mediated self-healing process of a damaged magnetoresistive composite in water (from left to right): d1) water was poured into a beaker where the damaged composite was placed; d2) the damaged magnetoresistive composite was completely soaked into water; d3) two segments of the damaged composite was reconnected, driven by the AMF induced attracting force; d4) self-healing was carried out through the dynamic reformation of chemical bonds and the entanglement of the polymer chains (driven by AMF-induced Ni81Fe19 microparticle oscillations); d5) the damaged magnetoresistive composite was successfully healed in water. Scale bars: 1 cm.  According to the experimental results in panels a) and b), the relationship between magnetic field (MF) and magnetoresistance (MR) of printable sensor can be described by equation (1): (1) and the magnetic field (MF) as a function of distance (Dist) generated by a permanent magnet follows equation 2: In other words, as approaching permanent magnet, the printable sensor exhibits a distance dependent magnetoresistance, as defined by equation (3): Considering the practical operational situation, the distance and the magnetoresistance in the equation (3) have a one-to-one correspondence. Thus, we have Following the equation (4), the magnetoresistance signal can be converted into the distance between two fingers by software of numerical interpolation (here, using a linear interpolation).

Fig. S28
Operation of printable magnetoresistive sensor for augment reality (AR). a-g) Snapshots of Supplementary Movie 7: a) as the sensor-mounted forefinger is far away from a magnet mounted on a thumb, the electrical resistance of the magnetoresistive sensor is changed due to surrounding electromagnetic disturbances, which results in the fluctuation noise of the resistance signal. b) As two fingers get in touch, the sensor resistance increases sharply to cross a preset threshold and consequently the system of AR glasses will be started. c) Programs pop up on the lenses. d) As approaching fingers, the sensor resistance is changed. Supposing a one-to-one correspondence between resistance value and programs, various programs can be scanned with changing the distance between forefinger and thumb. e) At a specific distance, the program of interest (here, video player) is selected after holding the fingers for several seconds. f) As two fingers are in contact again and the sensor resistance becomes higher than the threshold value, the program of video player is activated. g) Video is playing on the lenses. Scale bars: 5 cm.   The fabrication process and magnetic characterization of Ni97Co3-composite based magnetoresistive sensor is the same as that used for printable Ni81Fe19 magnetoresistive sensor. An arbitrary 1 g/ml was used for the filler concentration of composite solution. The electrical resistance of the magnetoresistive element at 0 mT is 24.8 Ω. The fabrication process and magnetic characterization of Fe-composite based magnetoresistive sensor is the same as that used for printable Ni81Fe19 magnetoresistive sensor. An arbitrary 1 g/ml was used for the filler concentration of composite solution. The presence of oxygen element in EDX map (panel c)) came from the oxidization of iron at the microparticle surfaces. Although the thin oxide layer was adverse to the electrical percolation between neighboring Fe microparticle, the AMF-induced intimate connection still can overcome this problem and generate magnetoresistive performance. The electrical resistance of the magnetoresistive element at 0 mT is 12.4 Ω. As the polymeric binders of PDMS and PBS were dissolved in a solvent, the viscosity of the binder solutions can be tuned that is desirable for dispersion of Ni81Fe19 microparticles in the whole volume after shaking ( Supplementary Fig. 33a). In contrast, as the binders were not diluted by the solvent, the composite exhibited very high viscosity. Consequently, Ni81Fe19 microparticles cannot be dispersed by shaking and always concentrated at the bottom of the composite ( Supplementary  Fig. 33b). It is worth noting that because of the high viscosity, air bubbles were easily generated in the binder without solvent during agitating that are not visually observed in the low-viscosity binder solutions diluted by solvent ( Supplementary Fig. 33c,d). Therefore, the addition of solvent into the composite is crucial for forming the electrical percolation pathways in the following printing steps. Supplementary Fig. 33e, f compare the electrical resistances of two segments of a printed trace based on the diluted binders. Two resistance values for the same length of 5 mm are 112.3 and 108.2 Ω, respectively. Considering the roughness variation of the plastic substrate, the small resistance deviation of about 2% indicates the homogeneous dispersion of microparticles in the printed composite. The homogeneity of the microparticle dispersion can be further verified by SEM images of the printed composite in which no obvious agglomeration of microparticles is observed ( Supplementary Fig. 33g). Statistical analysis points out that voids without Ni81Fe19 microparticles only account for a 5.6% surface coverage. In particular, these voids are randomly distributed in the whole space and isolated from each other, thus avoiding the blocking of electrical conductance along the printed trace.